The Borg Ground Invasion happens on the planet Defera on specific times on specific dates. Check the calender for the times. Brandon (PWE_BranFlakes) will occasionally put together a ground event, where captains will come together and group up. Check the forums or the REDALERT chat channel for details. It'll usually happen for the first hour of the event. Note that unlike STFs, Klingon and Federation players cannot group together.
The Borg Ground Invasion happens for two hours (Occasionally 4 hours on weekends when indicated). That means you have two hours to complete everything you want or farm as much Borg samples as you can. Once the time limit is reached, everyone will be returned to base camp, and the Borg will disappear back into the Probe. You're missions will be dropped. This means you'll have to do all the missions over from scratch each time the invasion occurs.
The Invasion is separated into five different locales on the same map. Base Camp is the hub where everyone beams in at the start. From here you get the quests for the other four locations. There's a crafting vendor with special items for crafting that are specially tailored to fighting the Borg. You'll need to collect Borg components from dead Borg to craft them. There's also a mail console at the back. You could potentially walk to each of the other four locations from Base Camp. The easiest way however, is to jump into the action by taking the transporter pads.
Each location (except the Probe) has Easy, Medium, and Hard Missions. You have to first complete ONE easy mission to unlock the medium missions, and ONE medium mission to unlock the hard mission. After completing one hard mission for either City, Temple, or Power Plant, you'll unlock the Hard mission for the Sphere.
A note on Sharing missions. It's possible to share missions, for instance sharing a hard with someone who has to finish medium first. If they accept, they won't be able to turn in the mission. If you want to get credit for doing the mission, you first have to complete a medium mission, turn it in, then accept the shared mission. Otherwise it will count as a secondary even if you've completed a medium after accepting, and won't be able to claim the reward.
EXTREMELY BIG IMPORTANT REMINDER: Bring a remodulator to this instance. You can craft a better one at the crafting station, but the Borg can and will adapt to your weapons. This will make it especially difficult fighting any Borg, since you can't do much damage against them when they've adapted. Remodulators can be gotten through your Replicator in space. They're at the top of the list, and they're free. If you don't have one, try asking around for one in Zone, sometimes generous people have spare remodulators to hand out. You can get ONE remodulator at the start by telling the Base Camp commander you don't have a remodulator.